Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Arrange the shapes in a line so that you change either colour or
shape in the next piece along. Can you find several ways to start
with a blue triangle and end with a red circle?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
This activity investigates how you might make squares and pentominoes from Polydron.
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
An activity making various patterns with 2 x 1 rectangular tiles.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Investigate the different ways you could split up these rooms so
that you have double the number.
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
What is the best way to shunt these carriages so that each train
can continue its journey?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
How many models can you find which obey these rules?
Can you use the information to find out which cards I have used?
How many trapeziums, of various sizes, are hidden in this picture?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
How many different triangles can you make on a circular pegboard that has nine pegs?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?